算法随笔——欧拉回路

学习链接
oiwiki

定义

判别方法

注意是要边联通，有孤立点也可以有欧拉路

P7771 【模板】欧拉路径(有向图)

P7771 【模板】欧拉路径

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define INF 0x3f3f3f3f
#define re register
#define PII pair<int,int>
int read()
{
	int f=1,k=0;char c = getchar();
	while(c <'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9')k=(k<<1)+(k<<3)+(c^48),c=getchar();
	return k*f;
}

const int N = 4e5+5;

int n,m;
vector<int> v[N];
int ing[N],deg[N];

int sta[N],top;

void dfs(int u)
{
	while (v[u].size())
	{
		int j = v[u].back();
		v[u].pop_back();//将该边删除
		dfs(j); // 继续跑dfs
	}
	sta[++top] = u;
}

int main()
{
	cin >> n >> m;
	for (int i = 1;i <= m;i++) 
	{
		int x = read(),y = read();
		v[x].push_back(y);
		ing[y]++,deg[x]++;
	}
	//先进行判定
	int cnt1 = 0 ,cnt2 = 0,S = 0; // S 为起点
	for (int i = 1;i <= n;i++)
	{
		sort(v[i].begin(),v[i].end(),greater<int>()); //先取尾所以倒序排序
		if (ing[i] != deg[i])
		{
			if (abs(ing[i]-deg[i])>1) 
			{
				puts("No");
				return 0;
			}
			else if (ing[i] > deg[i]) cnt1++;
			else cnt2++,S = i;
		}
	}
	
	if (cnt1 == cnt2)
	{
		if (cnt1 == 0) S = 1;
		dfs(S);
		for (int i = top;i >= 1;i--) cout << sta[i] << ' ';
		puts("");
	}
	else puts("No");
	
	
	return 0;
}

P1341 无序字母对（无向图）

P1341

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define INF 0x3f3f3f3f
#define re register
#define PII pair<int,int>
int read()
{
	int f=1,k=0;char c = getchar();
	while(c <'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9')k=(k<<1)+(k<<3)+(c^48),c=getchar();
	return k*f;
}
const int N = 2e5;
int n;
vector<PII > v[N];
int m;
bool vis[N];
int deg[N];
void add(int x,int y,int id)
{
	v[x].push_back({y,id});
	deg[y]++;
}
vector<int> ans;
void dfs(int u)
{
	while (v[u].size())
	{
		auto j = v[u].back().first;
		auto id = v[u].back().second;
		v[u].pop_back();
		if (!vis[id])
		{
			vis[id] = 1;
			dfs(j);
		}
	}
	ans.push_back(u);
}
int main()
{
	cin >> m;
	for (int i = 1;i <= m;i++)
	{
		char ch1,ch2;
		cin >> ch1 >> ch2;
		add(ch1,ch2,i);
		add(ch2,ch1,i);
	}
	int cnt1 = 0,cnt2 = 0,S = INF;
	int minS = INF;
	for (int i = 0;i <= 200;i++) sort(v[i].begin(),v[i].end(),greater<PII>());
	for (int i = 0;i <= 200;i++)
		if (deg[i])
		{
			minS = min(minS,i);
			if (deg[i] & 1) cnt1++,S = min(S,i);
			else cnt2++;
		}
	if (cnt1==0 || cnt1 == 2)
	{
		if (!cnt1) S = minS;
		dfs(S);
		reverse(ans.begin(),ans.end());
		for (auto it:ans) cout << (char)it ;
	}
	else puts("No Solution");
	
	return 0;
}